Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings

In this paper, we design two inertial-type subgradient extragradient algorithms with the linear-search process for resolving the two pseudomonotone variational inequality problems (VIPs) of and the common fixed point problem (CFPP) of finite Bregman relatively nonexpansive operators and Bregman rela...

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Bibliographic Details
Published in:Axioms 2023-09, Vol.12 (9), p.832
Main Authors: Wang, Cong-Shan, Ceng, Lu-Chuan, Li, Bing, Cao, Sheng-Long, Hu, Hui-Ying, Liang, Yun-Shui
Format: Article
Language:English
Subjects:
Algorithms
Banach spaces
Bregman distance
Bregman projection
Bregman relatively demicontractive mapping
Competitive advantage
Convexity
finite Bregman relatively nonexpansive mappings
Inequalities (Mathematics)
Mathematical research
modified inertial-type subgradient extragradient method
Operators
Search process
Smoothness
variational inequality problem
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Summary:In this paper, we design two inertial-type subgradient extragradient algorithms with the linear-search process for resolving the two pseudomonotone variational inequality problems (VIPs) of and the common fixed point problem (CFPP) of finite Bregman relatively nonexpansive operators and Bregman relatively demicontractive operators in Banach spaces of both p-uniform convexity and uniform smoothness, which are more general than Hilbert ones. By the aid of suitable restrictions, it is shown that the sequences fabricated by the suggested schemes converge weakly and strongly to a solution of a pair of VIPs with a CFPP constraint, respectively. Additionally, the illustrative instance is furnished to back up the practicability and implementability of the suggested methods. This paper reveals the competitive advantage of the proposed algorithms over the existing algorithms; that is, the existing hybrid projection method for a single VIP with an FPP constraint is extended to develop the modified inertial-type subgradient extragradient method for a pair of VIPs with an CFPP constraint.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12090832